Equation with two square roots (with a fake solution)

Equation with two square roots, with an extraneous solution,

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blackpenredpen
straightforward math lessons,

[SeeTv.]

4:19 this is where the fake solution appears. He creates a quadratic which can have more than one solution.
If you plug in 8 before it's wrong but from this step at 4:19 8 becomes an answer.

[Treegrower]

Hey, love your videos! Can you make one on finding the concavity ranges and inflection points of a function?

[chetsia]

If you take the negative answer for the square root of 1. You will end up getting -1=-1 which makes x=1 true.

[wendeldickau]

Square root solutions can be plus or minus, the answer of x=1 works if the solution of the square roots is negative, so could x=1 be valid where square root solution is negative? Likewise x=8 only works when solution to the roots are positive.?

[fiafjs]

Hey, do you think you are going to continue those calculus videos you used to do? They are very helpful

[ongyiumark]

why dont you take into account the negative roots

[petterhouting]

sqrt(1) = 1+ sqrt(4)
sqrt(1)= 1 and -1 because (1)^2 and (-1)^2 are both 1
sqrt(4) = 2 and -2 because (2)^2 and (-2)^2 are both 4

sqrt(1)=1+sqrt(4)
(1 or -1) = 1+ (2 or -2)

if you choose -1 and -2 then the equation is correct
-1=1+-2
+8:33
so 1 is not fake
a square root always is a positive AND negative, many people forget that

+9:54 x is also equal to 1 above is my explanation

ok here is the extra proof for x = 1

sqrt(5x-4)=1+sqrt(3x+1)
sqrt(5-4)=1+sqrt(3(1)+1)
sqrt(5-4)=1+sqrt(3+1)
sqrt(1)=1+sqrt(4)
plusminus(1)=1 plus plusminus(2)
-1=1+-2
-1=1-2

[joshsmit]

why did you get a false answer if you followed all of the rules ?

[lzuluaga]

Qué de extraordinario tiene eliminar unos simples radicales cuadráticos? Nada!!!

[jimmycastro]

Maybe that's wrong because you forgot de abs value XD